Type with curvy front face / round front bevel
By tweaking both the Bevel Depth and Modification Offset you should be able to achieve quite good results:



Start by increasing the depth: the font will increse its outline while creating the curved. Then use a negative offset value to compensate this growth and to make the flat face as small as possible. the You should also ensure that the beveling resolution is high enough in order to achieve the wanted smooth surface.

Then you could convert the text object to a mesh. This way you'll have more control upon the shading of the sharp edges. I marked them manually in the following example: